Highest median voting rules

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The highest median voting rules are a class of graded voting rules where the candidate with the highest median rating is elected.

The various highest median rules differ in their treatment of ties, i.e., the method of ranking the candidates with the same median rating.

Proponents of highest median rules argue that they provide the most faithful reflection of the voters' opinion. They note that as with other cardinal voting rules, highest medians are not subject to Arrow's impossibility theorem, and so can satisfy both independence of irrelevant alternatives and Pareto efficiency.

However, critics note that highest median rules violate participation and the Archimedean property; highest median rules can fail to elect a candidate almost-unanimously preferred over all other candidates.